The present investigation deals with the natural, mixed and forced convection in a vented rectangular cavity having a sinusoidal heated vertical wall with a conducting solid block placed at one of the nine positions. The objective is to analyze numerically using finite element method the effects of the following parameters: inlet, outlet positions, solid square positions, thermal coefficient λ, amplitude ratio ɛ, phase deviation ϕ and the solid square size on the thermo-convective flows. The Richardson number is varied from 0 to 40, the Reynolds and Prandtl numbers are fixed respectively at 100 and 0.71. To quantify the heat transfer of the solid block and to get closer to real conditions, we have developed a modification based on the evaluation of the Nusselt number using the average temperature in the cavity, unlike previous works which used the input temperature. As results, the sinusoidal temperature at the right wall gives higher heat transfer enhancement. The variation of the phase deviation and amplitude ratio have a slightly effect on the average fluid temperature and average Nusselt at the right wall and at the square solid.

This work presents a study by numerical simulation of mixed convection in a rectangular cavity with a sinusoidal temperature imposed on the right vertical wall while the other wall on the left is kept at a cold temperature. The upper and lower walls are thermally insulated, the inlet and outlet ports are respectively located on the hot wall to the bottom and on the top to the left. The enclosure represents a practical system such as an air-cooled electronic device, the heat source represents a radiator or an electronic component located in three different positions towards the left side at the bottom, the center and towards the right side at the top in such an enclosure. All calculations are made for a range of Richardson number from 0 to 10 and Reynolds numbers from 50 to 200. The influence of Richardson number, the position of the heat source and the influence of amplitude and phase deviation of the temperature imposed on the Nusselt number on the hot surface is studied. The results are presented in the form of streamlines and isotherms graphs as well as the variation in maximum temperature and mean Nusselt number under different conditions. The numerical resolution of the governing equations is obtained using the software of Multiphysics Comsol based on the finite element method.